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            <h1 style="display: none">【转】一道看似简单的面试题</h1>
            
            <div class="markdown-body">
              <p>原文链接:<br><a target="_blank" rel="noopener" href="https://segmentfault.com/a/1190000015718348">一道看似简单的面试题</a></p>
<h1 id="前言"><a href="#前言" class="headerlink" title="前言"></a>前言</h1><pre><code>使用PHP,给定一个数,判断这个数是否是二的N次方
</code></pre>
<p>这样看似简单的一个面试题, 实际牵出了很多基础知识,本章在为大家补习基础知识的情况下来解答这道题。先亮出答案</p>
<figure class="highlight php"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><code class="hljs php"><span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">exponentiation</span>(<span class="hljs-params"><span class="hljs-variable">$number</span></span>)</span><br><span class="hljs-function"></span>&#123;<br>    <span class="hljs-keyword">if</span> (<span class="hljs-variable">$number</span> &lt; <span class="hljs-number">0</span>) &#123;<br>        <span class="hljs-keyword">return</span> <span class="hljs-literal">false</span>;<br>    &#125;<br>        <br>    <span class="hljs-keyword">if</span> ((<span class="hljs-variable">$number</span> &amp; (<span class="hljs-variable">$number</span> - <span class="hljs-number">1</span>)) == <span class="hljs-number">0</span>) &#123;<br>        <span class="hljs-keyword">return</span> <span class="hljs-literal">true</span>;<br>    &#125; <span class="hljs-keyword">else</span> &#123;<br>        <span class="hljs-keyword">return</span> <span class="hljs-literal">false</span>;<br>    &#125;<br>&#125;<br>    <br>exponentiation (<span class="hljs-number">2</span>);     <span class="hljs-comment">// bool(true)</span><br>exponentiation (<span class="hljs-number">8</span>);     <span class="hljs-comment">// bool(true)</span><br>exponentiation (<span class="hljs-number">16</span>);    <span class="hljs-comment">// bool(true)</span><br>exponentiation (<span class="hljs-number">32</span>);    <span class="hljs-comment">// bool(true)</span><br>exponentiation (<span class="hljs-number">128</span>);   <span class="hljs-comment">// bool(true)</span><br></code></pre></td></tr></table></figure>
<p><strong>这是查阅后的最最标准的答案，其他类似通过循环等等答案就略过把。</strong></p>
<h1 id="运算"><a href="#运算" class="headerlink" title="运算"></a>运算</h1><p>实际这道面试题考的并非是算法，而是作为开发人员的你“底子”够不够。</p>
<p>运算符应该是每门语言hello world 后立马要学习的。运算符分很多种，赋值运算符，比较运算符等等。我想大多自学或者培训出道的没有经过系统化学习的童鞋的，对这块的知识应该很薄弱把。当然赋值、比较什么的很熟悉，因业务基本逃不过这些。</p>
<p>但对位运算符，你真的吃透了吗？</p>
<pre><code>这道题的考点一是位运算符的使用，上面说过了本题考察的并非算法，而是你对二进制的了解，而在php中能操作二进制的运算符貌似 (我的知识范围内) 只有位运算符
</code></pre>
<h2 id="PHP位运算符-部分"><a href="#PHP位运算符-部分" class="headerlink" title="PHP位运算符 (部分)"></a>PHP位运算符 (部分)</h2><p>本道面试题用到了 &amp; 所以不详解其他的运算符，需要更多了解请移步官方</p>
<p><a target="_blank" rel="noopener" href="http://php.net/manual/zh/language.operators.bitwise.php">http://php.net/manual/zh/lang…</a></p>
<table>
<thead>
<tr>
<th>运算符</th>
<th>附加信息</th>
</tr>
</thead>
<tbody><tr>
<td>&amp;</td>
<td>按位与运算符</td>
</tr>
<tr>
<td>^</td>
<td>按位异或运算符</td>
</tr>
</tbody></table>
<h1 id="按位与"><a href="#按位与" class="headerlink" title="按位与"></a>按位与</h1><p>按位与以简单易懂的方式来讲就是二进制位不相同的抵消，相同的保留</p>
<p><img src="/images/php/bitwise-and.png" srcset="/img/loading.gif" lazyload alt="按位与"></p>
<p>举几个栗子</p>
<pre><code>公式 -&gt; 转为二进制后的公式 -&gt; 二进制结果 -&gt; 十进制结果
</code></pre>
<hr>
<pre><code>2 &amp; 3 -&gt; 0010 &amp; 0011 -&gt; 0010 = 2
10 &amp; 7 -&gt; 1010 &amp; 0111 -&gt; 0010 = 2
32 &amp; 70 -&gt; 0100000 &amp; 1000110 -&gt; 0000000 = 0
</code></pre>
<h1 id="按位异或"><a href="#按位异或" class="headerlink" title="按位异或"></a>按位异或</h1><p><img src="/images/php/bitwise-xor.png" srcset="/img/loading.gif" lazyload alt="按位异或"></p>
<p>举几个栗子</p>
<pre><code>公式 -&gt; 转为二进制后的公式 -&gt; 二进制结果 -&gt; 十进制结果
</code></pre>
<hr>
<pre><code>2 ^ 3 -&gt; 0010 ^ 0011 -&gt; 0001 = 1
10 ^ 7 -&gt; 1010 ^ 0111 -&gt; 1101 = 13
32 ^ 70 -&gt; 0100000 ^ 1000110 -&gt; 1100110 = 102
</code></pre>
<h1 id="进制"><a href="#进制" class="headerlink" title="进制"></a>进制</h1><p>借用百度百科上的一段话</p>
<pre><code>二进制是计算技术中广泛采用的一种数制。二进制数据是用0和1两个数码来表示的数。它的基数为2，进位规则是“逢二进一”，借位规则是“借一当二”。
</code></pre>
<p>二进制本身就是为2这个数字而使用的，所以说这道面试题直指二进制的使用是没错的。2的n次方则就是</p>
<table>
<thead>
<tr>
<th>n</th>
<th>公式</th>
<th>结果</th>
</tr>
</thead>
<tbody><tr>
<td>1</td>
<td>2</td>
<td>2</td>
</tr>
<tr>
<td>2</td>
<td>2x2</td>
<td>4</td>
</tr>
<tr>
<td>3</td>
<td>2x2x2</td>
<td>8</td>
</tr>
<tr>
<td>4</td>
<td>2x2x2x2</td>
<td>16</td>
</tr>
</tbody></table>
<p>换算成二进制的表格是</p>
<table>
<thead>
<tr>
<th>n</th>
<th>公式</th>
<th>结果</th>
</tr>
</thead>
<tbody><tr>
<td>1</td>
<td>2</td>
<td>000010</td>
</tr>
<tr>
<td>2</td>
<td>2x2</td>
<td>000100</td>
</tr>
<tr>
<td>3</td>
<td>2x2x2</td>
<td>001000</td>
</tr>
<tr>
<td>4</td>
<td>2x2x2x2</td>
<td>010000</td>
</tr>
</tbody></table>
<p>由此看出2的n次方的二进制最高位是1，其余补0，(n&amp;(n-1))==0 并且 n&gt; 0 的情况下必定是2的n次方，为什么要-1呢？在二进制中每一位必须都不相同&amp;后才会得出0，上述已经讲解了&amp;的运算结果。例如十进制的16</p>
<pre><code>16 &amp; (16 - 1) = 
010000 &amp; (001111) = 0 
</code></pre>
<p>不要纠结(n&amp;(n-1))==0 这个公式是怎么来的，作为程序员，我感觉应该把更多时间放到反推上面来，去应证这个公式的正确性。</p>
<pre><code>验证是否是2的n次方，笨的方法就是一直除2，除到最后等于0则就是2的次方，所以公式如上
</code></pre>
<h1 id="补位"><a href="#补位" class="headerlink" title="补位"></a>补位</h1><p>如果是2个二进制进行运算时，计算机会统一位数，例如</p>
<pre><code>01
011
&lt;------&gt; 
001
011
</code></pre>
<p>计算机会将01自动补一位为001去方便运算。</p>
<h1 id="正负"><a href="#正负" class="headerlink" title="正负"></a>正负</h1><p>在二进制中，第一位为1的是负数，0是正数。如果没有补零的情况下</p>
<pre><code>10000000000
01111111111
</code></pre>
<p>虽然计算后也是0，但它并不是2的n次方，因为第一组二进制是负数。</p>
<h1 id="补充"><a href="#补充" class="headerlink" title="补充"></a>补充</h1><pre><code>给定任意数，计算是2的几次方？
</code></pre>
<figure class="highlight php"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br></pre></td><td class="code"><pre><code class="hljs php"><span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">power</span>(<span class="hljs-params"><span class="hljs-variable">$number</span></span>)</span>&#123;<br>    <span class="hljs-keyword">if</span> (<span class="hljs-variable">$number</span> &lt; <span class="hljs-number">0</span>) &#123;<br>        <span class="hljs-keyword">return</span> <span class="hljs-literal">false</span>;<br>    &#125;<br>    <br>    <span class="hljs-keyword">if</span> ((<span class="hljs-variable">$number</span> &amp; (<span class="hljs-variable">$number</span> - <span class="hljs-number">1</span>)) == <span class="hljs-number">0</span>) &#123;<br>        <br>        <span class="hljs-comment">// 数学不好的,就看下面的方法</span><br>        <span class="hljs-comment">// $number = decbin($number);</span><br>        <span class="hljs-comment">// return (mb_strlen($number)-1);</span><br>        <span class="hljs-comment">// 数学可以的就看下面的方法</span><br>        <span class="hljs-keyword">return</span> floor(log(<span class="hljs-variable">$number</span>,<span class="hljs-number">2</span>));<br>    &#125; <span class="hljs-keyword">else</span> &#123;<br>        <span class="hljs-keyword">return</span> <span class="hljs-literal">false</span>;<br>    &#125;<br>&#125;<br></code></pre></td></tr></table></figure>
<ul>
<li>判断是否是2的n次方</li>
<li>如果是则将十进制数字转为二进制</li>
<li>计算总长度-1获取到是2的几次方,按照0的个数来计算</li>
</ul>
<p>原文链接:<br><a target="_blank" rel="noopener" href="https://segmentfault.com/a/1190000015718348">一道看似简单的面试题</a></p>

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